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Mosc. Math. J., 2005, Volume 5, Number 2, Pages 399–414 (Mi mmj201)  

This article is cited in 1 scientific paper (total in 2 paper)

Poincaré inequalities for maps with target manifold of negative curvature

T. Kappelera, V. Schroedera, S. B. Kuksinbc

a Institut für Mathematik, Universität Zürich
b Steklov Mathematical Institute, Russian Academy of Sciences
c Department of Mathematics, Heriot Watt University

Abstract: We prove that for any given homotopic $C^1$-maps $u,v\colon G\to M$ in a nontrivial homotopy class from a metric graph into a closed manifold of negative sectional curvature, the distance between $u$ and $v$ can be bounded by $3(length(u)+length(v))+C(\kappa,\varrho/20)$, where $\varrho>0$ is a lower bound of the injectivity radius and $-\kappa<0$ an upper bound for the sectional curvature of $M$. The constant $C(\kappa,\varepsilon)$ is given by
$$ C(\kappa,\varepsilon)=8\sh_\kappa^{-1}(1)+8\sh_\kappa^{-1}(\varepsilon)) $$
with $\sh_\kappa(t)=\sinh(\sqrt{\kappa}t)$. Various applications are given.

Key words and phrases: Negative sectional curvature, short homotopies, Poincaré inequality.

DOI: https://doi.org/10.17323/1609-4514-2005-5-2-399-414

Full text: http://www.ams.org/.../abst5-2-2005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 53C21, 55P99, 26D10
Received: October 27, 2003
Language:

Citation: T. Kappeler, V. Schroeder, S. B. Kuksin, “Poincaré inequalities for maps with target manifold of negative curvature”, Mosc. Math. J., 5:2 (2005), 399–414

Citation in format AMSBIB
\Bibitem{KapShrKuk05}
\by T.~Kappeler, V.~Schroeder, S.~B.~Kuksin
\paper Poincar\'e inequalities for maps with target manifold of negative curvature
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 2
\pages 399--414
\mathnet{http://mi.mathnet.ru/mmj201}
\crossref{https://doi.org/10.17323/1609-4514-2005-5-2-399-414}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200758}
\zmath{https://zbmath.org/?q=an:1093.53037}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595300006}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kokarev G., “On Geodesic Homotopies of Controlled Width and Conjugacies in Isometry Groups”, Group. Geom. Dyn., 7:4 (2013), 911–929  crossref  mathscinet  zmath  isi  elib  scopus
    2. C. Wayne, T. Kappeler, G. Kokarev, W. Craig, A. Piatnitsky, I. Chueshov, A. Shirikyan, L. H. Eliasson, “Sergei Borisovich Kuksin (on his 60th birthday)”, Russian Math. Surveys, 71:1 (2016), 167–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Moscow Mathematical Journal
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